Zero Order Reaction

Zero-order kinetics are always a product of the conditions under which the reaction is carried out. Therefore, reactions that follow zero-order kinetics are usually alluded to as pseudo-zero-order reactions. Obviously, the zero-order process cannot continue after the reactants are exhausted. Just before reaching this point, the reaction will revert to another rate law, rather than dropping straight to zero, as shown in the upper left corner.

Two general terms and conditions can result in a zero-order rate:

1- Only a small fraction of reactant molecules are in positions or states where they can react, and this fraction of molecules are constantly replenished from a larger pool.

2- When two or more reagents are involved, some reagents are much more concentrated than others

This usually occurs when reactions are catalysed by attachment to solid surfaces (heterogeneous catalysis) or enzymes.

Zero Order Reaction

Zero-order reaction kinetics in chemistry defines the rate of chemical reaction of reactants and products per unit time. It has nothing to do with the concentration of reactants. Chemical kinetics is related to the rate and reaction mechanism in terms of reactant and product molecules. In chemical equilibrium, only initial and final states are considered. The relationship between reactants and products is given by the law of mass action, and the energy relationship is determined by the laws of thermodynamics. 

Examples: At about 575°C, the nitrous oxide decomposes exothermically into nitrogen and oxygen 

2N2O-→2N2(g)+O2(g) 

This reaction in the presence of hot platinum wire (as a catalyst) is zero-order, but follows more traditional second-order kinetics when performed entirely in the gas phase.

2N2O⟶2N2(g)+O2(g)

Rate Law Expression

In kinetics, the rate of a chemical reaction is usually expressed in terms of reactants and products. Therefore, the concentration of reactants decreases and the product increases. When these decrease or increase the concentration expressed per unit time, we discover the velocity law in chemical kinetics.

A → product

Rate of reaction = – d[A]/dt = k[A]n

In some surface reactions, the rate was found to be independent of concentration. These reactions are called zero-order kinetics.

The Comprehensive Rate Law For Zero-Order Reactions

Consider a chemical reaction with initial concentrations of reactants = a and products = 0. Elapsed time t, concentration of reactants = (a – x), product = x. Therefore, the concentration decreases after time t = x.

The rate in terms of product,

dx/dt = k0

where k0 = rate constant.

Or, dx = k0dt

When we integrate the above equation to the limit, the resulting rate equation for the reaction, x = k0t + c, where c = the integration constant. But when t = 0, which is the initial state of the reaction, x = 0. The integral constant (c) of the above equation is equal to 0. So x = k0t. It is a formula that expresses the decrease or increase in the concentration of reactants or products over time.

Differential Form of Zero-Order Reaction

Let initial concentration of reactants = [A]0 and elapsed time t = [A], so the rate equation for reactants, 

– d[A]/dt = k0 × [A]0 =k0

Negative sign, since the concentration decreases with time, the initial concentration of the reactant [A]0 = 0. 

Or, – d[A] = k0dt

Integrate the above equations

∫d[A] = k0 ∫dt

∴ – [A] = k0t + c

where c = integral constant.

If initial reactant concentration = [A]0 when time = 0, which is the initial time, – [A]0 = 0 + c and [A] = – [A]0. Therefore, the integral velocity equation for zero-order dynamics is,

– [A] = k0t – [A]0

Or, [A]0 – [A] =k0t 

This is another form of the zero-order kinetic velocity equation.

Zero-Order Half-Life

Half-life means that 50% of the reactant disappears within this time interval. When t = t½, this is the half-life to complete the reaction, i.e. the concentration of the reactants, [A] = [A]/2. 

Therefore [A]/2 = k0 × t½

Or, t½ = [A]/2k

It can be seen from the above formula that the half-life of zero-order kinetics depends on the initial concentration of the reactants.